EDB — 0G7

[0G7] Let \(A,B⊆ X\) be two subsets.

1. The interior of \(A\), denoted by \({{A}^\circ }\), is the union of all the open sets contained in \(A\), and therefore is the biggest open set contained in \(A\);

2. the closure of \(B\), denoted by \(\overline{B}\), is the intersection of all the closed sets that contain \(B\), i.e. is the smallest closed that contains \(B\).

3. We say that \(A\) is dense in \(B\) if \(\overline A ⊇ B\). ¹

4. The boundary \(∂ A\) of \(A\) is \(∂ A=\overline A⧵ {{A}^\circ }\).